What is the objective of performing principal component analysis?

The objective of performing principal component analysis (PCA) is to reduce dimensionality while preserving as much variance as possible in the data set. PCA transforms the original variables into a new set of variables called principal components, which are uncorrelated and ordered so that the first few retain most of the variation present in the original data.

Dimensionality reduction is crucial, especially when dealing with high-dimensional data, as it helps to simplify the data without losing significant information. By focusing on the components that account for the most variance, PCA helps to eliminate noise and redundancy in the dataset, making it easier to analyze and visualize.

The other options relate to different statistical techniques or analyses. Calculating the mean of the data is focused on central tendency and does not involve transforming the data's dimensional space. Conducting regression analysis is aimed at modeling relationships between variables rather than simplifying the structure of the data. Visualizing linear relationships might be a subsequent step after dimensionality reduction but is not the primary goal of PCA itself. Thus, reducing dimensionality while maintaining variance is central to the purpose of applying PCA.